After the intervention, posttest differences in identifying patterns in a function table were only marginally significant at grade 3, but experimental fifth graders more often described covariational relationships than recursive patterns¶

Claim · All claims
Evidence · 1 study (2 entries) · causal r1–r2 · q3
Currency · newest study 2011 · not yet checked against its sources · not reviewed by a person

Subclaims¶

q3 i? Overall posttest differences in providing a correct pattern or relationship description were only marginally significant at grade 3. → Stephens 2011 q3 i? By fifth grade, more experimental students provided covariational descriptions than recursive patterns, suggesting the teaching experiment encouraged considering relationships between variables. → Stephens 2011 (2)

Evidence¶

Stephens 2011¶

Stephens, A. C., Isler, I., Marum, T., Blanton, M. L., Knuth, E. J., & Gardiner, A. M. (2011). From recursive pattern to correspondence rule: Developing students' abilities to engage in functional thinking. https://eric.ed.gov/?id=ED585054

q3 · i? · causal · r1

Analysis of part b of the Brady task (Table 2), where students described patterns in a completed function table; total correct proportions rose for experimental students at all grades, but the article reports only marginal significance at grade 3.

"2verall posttest di fferences Zere only marginally significant at grade 3."

Stephens 2011 (2)¶

Stephens, A. C., Isler, I., Marum, T., Blanton, M. L., Knuth, E. J., & Gardiner, A. M. (2011). From recursive pattern to correspondence rule: Developing students' abilities to engage in functional thinking. https://eric.ed.gov/?id=ED585054

q3 · i? · causal · r2

Authors' interpretation of Table 2 response-category proportions: in grade 5 the experimental covariational proportion (.409) exceeded the recursive proportion (.386) at posttest, which the authors read as the intervention encouraging attention to relationships between variables.

"1ote that by fifth grade, more stXdents in the e[perimental groXp Zere providing sXch responses than Zere identifying recXrsive patterns, sXggesting the C7( sXccessfXlly encoXraged them to consider relationships betZeen variables."

Discussion¶

Learner Variables¶

• Algebraic Thinking — outcome: instruction changes it

Related Claims¶

• Experimental students significantly outperformed control students at posttest in expressing a functional relationship in words (grades 3-4) and in symbols (all grades), with no students writing correct symbolic rules at pretest — related
• Grades 3-4 students in an EALP-based early algebra intervention made significant improvements in constructing function tables and outperformed control students at posttest — related
• On a 'far' prediction to 10 tables, both conditions improved with no significant posttest differences in correctness, but the experimental group increasingly used a function rule as its strategy — related
• The authors conclude that elementary students are capable of sophisticated functional thinking and that this calls into question the lack of focus on covarying quantities in many elementary curricula and standards — a broader claim this one bears on